Fluid turbulence and eddy viscosity in relativistic heavy-ion collisions

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Abstract

The eddy viscosity for a turbulent compressible fluid with a relativistic equation of state is derived. Compressibility allows for sound modes, but the eddy viscosity in the shear mode is found to be the same as for incompressible fluids. For two space dimensions (which is the relevant case for the dynamics of relativistic heavy-ion collisions) the eddy viscosity in the shear mode is negative, reducing the effective viscosity below its microscopic value. This could explain the tiny viscosity found at RHIC. Implications for the experimentally accessible elliptic flow coefficient at the LHC are speculated on.

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Viscosity in Strongly Interacting Quantum Field Theories from Black Hole Physics

A Starinets, D. Son, P. Kovtun (2004)

The ratio of shear viscosity to volume density of entropy can be used to characterize how close a given fluid is to being perfect. Using string theory methods, we show that this ratio is equal to a universal value of \(\hbar/4\pi k_B\) for a large class of strongly interacting quantum field theories whose dual description involves black holes in anti--de Sitter space. We provide evidence that this value may serve as a lower bound for a wide class of systems, thus suggesting that black hole horizons are dual to the most ideal fluids.

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Anisotropy as a signature of transverse collective flow

Jean-Yves Ollitrault (1992)

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Shear viscosity of strongly coupled N=4 supersymmetric Yang-Mills plasma

, , (2010)

Using the anti-de Sitter/conformal field theory correspondence, we relate the shear viscosity \eta of the finite-temperature N=4 supersymmetric Yang-Mills theory in the large N, strong-coupling regime with the absorption cross section of low-energy gravitons by a near-extremal black three-brane. We show that in the limit of zero frequency this cross section coincides with the area of the horizon. From this result we find \eta=\pi/8 N^2T^3. We conjecture that for finite 't Hooft coupling (g_YM)^2N the shear viscosity is \eta=f((g_YM)^2N) N^2T^3, where f(x) is a monotonic function that decreases from O(x^{-2}\ln^{-1}(1/x)) at small x to \pi/8 when x\to\infty.